Canonical Models of Adjoint Foliated Structures on Surfaces

Abstract

In this paper, we study adjoint foliated structures of the form $K_{\mathcal{F}}+D$ on algebraic surfaces and their minimal and canonical models. We investigate the effective behavior of the linear systems $|m(K_{\mathcal{F}}+D)|$ for sufficiently divisible $m>0$. As an application, we obtain an effective answer to a boundedness problem for foliated surfaces of general type posed by Hacon and Langer.

36 pages, 5 figures. Author's final version. Accepted for publication in Journal of the London Mathematical Society